Given the functions \( h(x) = x^2 + 4x - 5 \) and \( g(x) = 4x - 4 \), there are several operations and analyses we can perform, such as addition, subtraction, composition, or finding points of intersection.

Let me know if you want to perform any specific operation, or if you need the solutions for specific \( x \) values. 

Would you like details on any of these aspects? Here are some questions we can explore:

1. What is \( h(x) + g(x) \)?
2. What is \( h(x) - g(x) \)?
3. What is the composition \( (h \circ g)(x) \)?
4. What is the composition \( (g \circ h)(x) \)?
5. What are the roots (zeros) of \( h(x) = 0 \) and \( g(x) = 0 \)?
6. Where do the graphs of \( h(x) \) and \( g(x) \) intersect?
7. What is the derivative of \( h(x) \) and \( g(x) \)?
8. How would you graph these functions on the same coordinate plane?

**Tip:** When working with functions, remember that compositions like \( (f \circ g)(x) \) substitute the output of \( g(x) \) into \( f(x) \), not vice versa.

Discover the operations and analyses of functions h(x) = x^2 + 4x - 5 and g(x) = 4x - 4. Explore addition, subtraction, composition, and intersections of these functions. Learn about derivatives and graphing on the same coordinate plane. Suitable for high school students.

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